Can you figure out how to help the rabbit travel one mile so he can go to his little home in the woods?

Question

A rabbit wants to hop 1 mile to his little home, but first he must past the half point of .5 miles, to get to that he must get to the midpoint of that which is .25 miles, but before that he must get to the .125 mile mark. However, unfortunately for the rabbit the 'midpoints' keep going on forever and ever because you can always take the decimal out to an infinite number of places. How can the rabbit ever get to his home if it is impossible to pass an infinite number of points in a finite amount of time?

Note to Washoe...fractions or decimals is irrelevant...you can convert the decimals into fractions if you want but they still have no end right?

You keep taking 'halves of the halves' which goes on infinitely....1/2, 1/4, 1/8,1/16,1/32,1/64,1/128, etc...

Answer 1

Begin with a leap of faith...

Answer 2

Mathematically, the scenario is impossible. You are using full integers and fractions that are 1/2, 1/4, 1/8-- which do not have an infinite number of decimal places.

My 10 year old son says the rabbit should just hop over the midpoints and be done with it.

Edit:
Nope, not true. Get a calculator and divide one by two. The calculator will not give you an infinite number if decimal places. Take the same calculator and divide 1 by 3-- you will then get an infinite number after .33333 (to infinity). Not all fractions infinitely repeat.

Edit II: OK, I give. You are way more tenacious and stubborn than I am.
My son says when you get to that point, its just time to blow up the midpoints and get that tired little bunny home.

Answer 3

This is a math question. I am with Carrie on this one. My eyes glazed over by then ".25 miles".

I am the stereotypical woman when it comes to numbers. I am totally inept at anything but the very basics. Now History and English... there I shine.

However, last night, one of our poodles, the female who has been retired from motherhood, came in from the gardens and gently dropped a very young rabbit in the whelping box with her sister's puppies! The puppies, eyes barely open, were still 20X bigger than the bunny. It was sooo cute.

It was old enough to be on its own because they are out on their own by 3 or 4 weeks of age so we returned it to the garden after much amazement and discussion.

Sorry, I am just not a math person so I thought I would tell you our bunny story instead. Now, perhaps I should pass this on to my girl who is working on her Masters in Math... it is not a genetic trait...smile.

Answer 4

solipsism or sophistry ?

"pick a card, any card"

"silly rabbit, keep hopping ... transfinite mathematics is for kids ... sophistry will never get you anywhere"

the number of points you describe has a 1-1 mapping with the integers (also the rationals) and thus has a cardinality of aleph-null [the "countable infinity"]

However, the total number of points he must traverse is uncountable [aleph-1, the "continuum", with a1-1 relationship with the real-numbers]

That being said, the entire notion of "number of points" is also irrelevant, since this semi-paradox leads one into a futile attempt to describe a quantity in a dimension by *any* number from a lower dimension.

"point" has dimensionality of zero
{Rsuperscript zero}

"line/length/distance" has dimensionality of one
{Rsuperscript 1}

"area" has dimensionality of two
{Rsuperscript 2}

etc

"Never let a philosopher design a mission-critical machine."

Answer 5

i hope youre talking about the baby bunny of mine (that lived w/my moms bf) that ran away on Thursday...poor Joshy and he was only 4 months old.
as long as hes happy, i will learn to accept that hes not coming back. if he found a home in the woods thats good.

im no good at math sry

Answer 6

Put one foot in front of the other
And soon you'll be walking 'cross the floor
Put one foot in front of the other
And soon you'll be walking out the door

Answer 7

I didn't understand a word you just said.

Answer 8

This question hurts my head...